Combined 4-component and relativistic pseudopotential study of ThO for the electron electric dipole moment search

Abstract

A precise theoretical study of the electronic structure of heavy atom diatomic molecules is of key importance to interpret the experiments in the search for violation of time-reversal (T) and spatial-parity (P) symmetries of fundamental interactions in terms of the electron electric dipole moment, eEDM, and dimensionless constant, k, characterizing the strength of the T,P-odd pseudoscalar-scalar electron-nucleus neutral current interaction. The ACME collaboration has recently improved limits on these quantities using a beam of ThO molecules in the electronic HΔ state [J. Baron et al., Science 343, 269 (2014)]. We apply the combined direct relativistic 4-component and two-step relativistic pseudopotential/restoration approaches to a benchmark calculation of the effective electric field, E, parameter of the T,P-odd pseudoscalar-scalar interaction, W, and hyperfine structure constant in Δ13 state of the ThO molecule. The first two parameters are required to interpret the experimental data in terms of the eEDM and k constant. We have investigated the electron correlation for all of the 98 electrons of ThO simultaneously up to the level of the coupled cluster with single, double, and noniterative triple amplitudes, CCSD(T), theory. Contributions from iterative triple and noniterative quadruple cluster amplitudes for the valence electrons have been also treated. The obtained values are E = 79.9 GV/cm, W = 113.1 kHz. The theoretical uncertainty of these values is estimated to be about two times smaller than that of our previous study [L. V. Skripnikov and A. V. Titov, J. Chem. Phys., 142, 024301 (2015)]. It was found that the correlation of the inner- and outer-core electrons contributes 9% to the effective electric field. The values of the molecule frame dipole moment of the Δ13 state and the HΔ→XΣ transition energy of ThO calculated within the same methods are in a very good agreement with the experiment.

Enhanced effect of CP -violating nuclear magnetic quadrupole moment in a HfF+ molecule

“…This means that the convergence with respect to correlation effects is achieved. Basis set correction on high-order harmonics is negligible (in contrast to the ThO case [19]). We estimate the accuracy of the final value of W M to be better than 4%.…”

“…This leads to considerable computational savings. Some technical advantage is that one can also use very compact contracted basis sets [19,37]. This is of crucial importance to treat high-order correlation effects.…”

“…In Refs. [19,50] we suggested to combine the two-step approach and the direct relativistic Dirac-Coulomb(-Gaunt) approach to take advantages of both approaches.…”

Calculation of the magnetic hyperfine structure constant of alkali metals and alkaline-earth-metal ions using the relativistic coupled-cluster method

“…The 1s-3d electrons also need much higher virtual energy orbitals for proper correlation functions as shown in Ref. [66,67]. A series of calculations are done to estimate the uncertainty associated with the Z-vector values of the magnetic HFS constant of these systems.…”

CHEMICAL SHIFTS OF X-RAY EMISSION SPECTRA AND EFFECTIVE STATES OF YTTERBIUM IN FLUORIDES: EMBEDDED CLUSTER MODELING OF YbF2 AND YbF3 CRYSTALS

“…[17]. Comparison of the two-step approach (in which the inner-core electrons are treated as frozen) with the all-electron treatment was made in papers [17][18][19], where an agreement on the level of accuracy of the used correlation methods is attained.…”